Math Problem Statement

A restaurant offers delivery for their pizzas. The total cost is a delivery fee added to the price of the pizzas. One customer pays $25 to have 2 pizzas delivered. Another customer pays $58 for 5 pizzas. How many pizzas are delivered to a customer who pays $80?

Solution

We can set up a system of equations to solve for the price of a pizza and the delivery fee.

Define Variables:

  • Let pp be the price of one pizza.
  • Let dd be the delivery fee.

Given Information:

  1. A customer pays $25 for 2 pizzas:
    2p+d=252p + d = 25
  2. Another customer pays $58 for 5 pizzas:
    5p+d=585p + d = 58

Solve for pp and dd:

Step 1: Subtract the first equation from the second:

(5p+d)(2p+d)=5825(5p + d) - (2p + d) = 58 - 25 3p=333p = 33 p=11p = 11

Step 2: Solve for dd:

Substituting p=11p = 11 into the first equation: 2(11)+d=252(11) + d = 25 22+d=2522 + d = 25 d=3d = 3

Step 3: Find the Number of Pizzas for $80:

Using the equation: xp+d=80xp + d = 80 x(11)+3=80x(11) + 3 = 80 11x=7711x = 77 x=7x = 7

Thus, a customer who pays $80 receives 7 pizzas.

Would you like more details or have any questions?

Related Questions:

  1. What would be the cost for 10 pizzas, including delivery?
  2. If the restaurant removes the delivery fee, how much would each customer pay per pizza?
  3. What if the delivery fee increased to $5? How would that affect the cost?
  4. Can you create a general formula for the cost of xx pizzas with a delivery fee?
  5. If a customer has $100, how many pizzas can they order?

Math Tip:

When solving systems of equations, elimination is a powerful method when the coefficients of one variable are the same or can be made the same.

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Equations
Linear Equations

Formulas

2p + d = 25
5p + d = 58
xp + d = 80

Theorems

Elimination Method for Solving Systems of Equations

Suitable Grade Level

Grades 8-10